Question

You are offered an investment with the following conditions:

• The cost of the investment is 1,000.
• The investment pays out a sum X at the end of the first year; this payout grows at the rate of 10% per year for 11 years.
If your discount rate is 15%, calculate the smallest X which would entice you to purchase the asset.

Answer 1

To calculate the smallest payout X for an investment to be enticing at a 15% discount rate, we use the present value formula and solve for X.

Step-by-step explanation:

To calculate the smallest X which would entice you to purchase the asset, we need to determine the present value of the investment at the discount rate of 15%. The payout for the investment grows at a rate of 10% per year for 11 years. Using the present value formula, the equation becomes:

X/{(1+0.15)^1} + X/{(1+0.15)^2} + ... + X/{(1+0.15)^11} = 1000

Solving this equation, we find that X = $311.53 (rounded to the nearest cent). Therefore, the smallest X that would entice you to purchase the asset is $311.53.